1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
german
3 years ago
15

Use Newton's method to estimate the requested solution of the equation. Start with given value of X0 and then give x2 as the est

imated solution.
x3 + 5x +2 = 0; x0 = -1; Find the one real solution.
Mathematics
1 answer:
levacccp [35]3 years ago
6 0

Answer:

<h2>-0.3913 </h2>

Step-by-step explanation:

Given the initial value of X0 = -1, we can determine the solution of the equation x³ + 5x +2 = 0 using the Newton's method. According to newton's approximation formula;

y = f(x_0) + f'(x_0)(x-x_0)

x_n = x_n_-_1  - \frac{f(x_n_-_1 )}{f'(x_n_-_1 )}

If x_0 = 1\\

We will iterate using the formula;

x_1 = x_0  - \frac{f(x_0 )}{f'(x_0 )}

Given f(x) = x³ + 5x +2

f(x0) = f(-1) = (-1)³ + 5(-1) +2

f(-1) = -1 -5 +2

f(-1) = -4

f'(x) = 3x²+5

f'(-1) = 3(-1)²+5

f'(-1) = 8

x_1 = -1+4/8\\x_1 = -1+0.5\\x_1 = -0.5\\\\x_2 = x_1 - \frac{f(x_1)}{f'(x_1)}\\x_2 = -0.5 - \frac{f(-0.5)}{f'(-0.5)}

f(-0.5) = (-0.5)³ + 5(-0.5) +2

f(-0.5) = -0.125-2.5+2

f(-0.5) = -0.625

f'(-0.5) = 3(-0.5)²+5

f'(-0.5) = 3(0.25)+5

f'(-0.5) = 0.75+5

f'(-0.5) = 5.75

x_2 = -0.5 - \frac{(-0.625)}{5.75}\\x_2 = -0.5 + \frac{(0.625)}{5.75}\\x_2 = -0.5 + 0.1086957\\x_2 = -0.3913

The estimated solution is -0.3913 (to 4dp)

You might be interested in
Choose an appropriate scenario for the graph below...
schepotkina [342]

Answer:

2. Tom ran from his house to the bus stop and waited. He realised that he missed the bus so he walked home

Step-by-step explanation:

He ran to the bus stop so his distance from his home is far, then he waited so the distance did not change, and then he went back home so the distance to the house got smaller again.

5 0
3 years ago
15 POINTS!!!!!!! What is the equation of the line in slope-intercept form? Line on a coordinate plane. Line runs through points
suter [353]

Answer:

y=\frac{4}{3}x+4 is the equation of line in slope intercept form.

Step-by-step explanation:

Line runs through points begin ordered pair negative 3 comma 0 end ordered pair and begin ordered pair 0 comma 4.

First ordered pair: (-3,0)

Second ordered pair: (0,4)

We have two points and need to find equation of line in slope intercept form

\text{Slope (m)}=\dfrac{y_2-y_1}{x_2-x_1}

\text{Slope (m)}=\dfrac{4-0}{0-(-3)}=\dfrac{4}{3}

y-intercept, when x=0 , (0,4)

Equation of line in slope intercept form:

y=mx+b

where, m=\frac{4}{3} and b=4

Required equation:

y=\frac{4}{3}x+4

Thus, y=\frac{4}{3}x+4 is the equation of line in slope intercept form.

3 0
3 years ago
Read 2 more answers
What number is 35% of 22
Ierofanga [76]
Go 0.35•22 and you get 7.7
8 0
3 years ago
Read 2 more answers
Use a net to find the surface area of the cone to the nearest square centimeter. Use 3.14 for pi (Round to nearest whole number)
Mariana [72]

Given:

The radius of the base of the given cone = 5 cm

The slant height of the cone = 19 cm

To find the surface area of the given cone.

Formula

The surface area pf the given cone is,

where, r be the radius and

l be the slant height.

Now,

Taking, r = 5, l = 19 and π = 3.14 we get,

sq cm

or,  sq cm

or,  sq cm

Rounding off to the nearest square centimeter, we get;

Hence,

The surface area of the cone is 377 sq cm.

3 0
3 years ago
What is the value of 324 + 435 + 546 when written in base 7?
Arada [10]
<span>The sum of 324, 435, and 546 is 1305. If this number were to be expressed by the base of 7, we would need to figure out what value of exponent would satisfy the requirement. This can be done by setting up an equation where 7 to the power of x must equal 1305. Using logarithms, one can solve for x and find it to be 3.6866853. Thus the sum of the aforementioned numbers, expressed in by the base of 7, is 7^3.6866853.</span>
6 0
3 years ago
Other questions:
  • Which function is represented by the graph below?
    14·1 answer
  • How many solutions does the equation |x+7|=-1 have
    14·1 answer
  • The circumference of a circle with an area of 1,809.56 square centimeters
    14·1 answer
  • Solve for x -3 + x <br> = - 38
    9·2 answers
  • Write the slope-intercept form of the equation of the line that has the same y-intercept as the black line shown and passes thro
    12·1 answer
  • 25/22 start fraction, 22, divided by, 25, end fraction of a number is what percentage of that number?
    9·1 answer
  • The system dx dt = −sx + sy dy dt = −xz + rx − y dz dt = xy − bz is the famous Lorenz system. It was developed as a model for we
    6·1 answer
  • IM ALMOST DONE WITH MY DIAGNOSTIC YAY!!!!​
    12·2 answers
  • What is the Y intercept of function g if g(x)=2f(x)+1? a. 0,3 b.0,2 c 0,1 d 0,-1​
    10·1 answer
  • Kate already owns 22 necklaces, and additional necklaces are priced at 2 for a dollar. With
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!